Problem: $f(t) = -5t+6-h(t)$ $g(n) = n+2(f(n))$ $h(x) = -4x-7$ $ g(h(-3)) = {?} $
Answer: First, let's solve for the value of the inner function, $h(-3)$ . Then we'll know what to plug into the outer function. $h(-3) = (-4)(-3)-7$ $h(-3) = 5$ Now we know that $h(-3) = 5$ . Let's solve for $g(h(-3))$ , which is $g(5)$ $g(5) = 5+2(f(5))$ To solve for the value of $g$ , we need to solve for the value of $f(5)$ $f(5) = (-5)(5)+6-h(5)$ To solve for the value of $f$ , we need to solve for the value of $h(5)$ $h(5) = (-4)(5)-7$ $h(5) = -27$ That means $f(5) = (-5)(5)+6-(-27)$ $f(5) = 8$ That means $g(5) = 5+(2)(8)$ $g(5) = 21$